Agree 100% My best example of that is Sanderson aking over the Wheel of Time after Jordan's passing. It was not perfect, especially in the earlier parts, but he respected the characters, understood them and genuinely wanted to complete Jordan's story and it shows.

Sadly Millennium 4 did not get this same treatment.

I read the first sequel and it was trailer trash bad, the characters where changed massively and the story made very little sense. I loved the original three so much that they are the only books I have ever read in the original Swedish (i had already read through in Norwegian once and the language is close enough that i could read without too many problems). I would heartily recommend not reading those so as to preserve the memory of the originals.

The sad part is that Larsson apparently almost finished a book 4 but due to family drama surrounding his death the draft seems to be stuck in limbo.